Publications

We present a homogeneous space geometry for the manifold of symmetric positive semidefinite matrices of fixed rank. The total space is a connected part of the general linear group endowed with its natural right-invariant metric and the metric on the homogeneous space is chosen such that the quotient space is the image of a Riemannian submersion from the total space. As a result, we obtain complete geodesics that are the image of certain ...

We present an algebraic multigrid algorithm for fully coupled implicit Runge-Kutta and Boundary Value Method time discretizations of the div-grad and curlcurl equations. The algorithm uses a blocksmoother and a multigrid hierarchy derived from the hierarchy built by any algebraic multigrid algorithm for the stationary version of the problem. By a theoretical analysis and numerical experiments, we show that the convergence is similar to or better ...

We describe an implementation technique for boundary element methods that greatly reduces the required number of evaluations of Green's function. Assuming that evaluating Green's function is a costly operation, our approach has a computational cost that is almost independent of the chosen discretization scheme. Nyström methods, collocation methods and Galerkin methods lead to similar computation times, although the latter requires the ...